(Reapproved 1994)

Guide for Determining the Fire ’ Endurance of Concrete Elements Reported by ACI Committee 216

Melvin S. Abrams Chairman W. J. McCoy Richard Muenow George E. Troxell G. M. Watson Roger H. Wildt N. G. Zoldners

Richard G. Gewain A. H. Gustaferro Tibor Z. Harmathy Lionel Issen Donald W. Lewis Howard R. May

Stanley G. Barton James E. Bihr Richard W. Bletzacker Merle E. Brander Boris Bresler John W. Dougill Frank G. Erskine The committee voting to revise this document was as follows:

Tibor Z. Harmathy Chairman Melvin S. Abrams Stanley G. Barton Richard W. Bletzacker Paul C. Breeze Boris Bresler John W. Dougill

William L. Gamble Richard G. Gewain Armand H. Gustaferro Tung D. Lin* Howard R. May

Jaime Moreno Richard A. Muenow Harry C. Robinson Thomas J. Rowe F. R. Vollert

*Chairman of the editorial subcommittee who prepared this report

This Guide for determining the fire resistance of concrete elements is a summary of practical information intended for use by architects. engineers and building officials who m u s t design concrete structures for particular fire resistances or evaluate structures as designed. The Guide contains information for determining the fire endurance of simply supported slabs and beams; continuous beams and slabs; floors and roofs in which restraint to thermal expansion occurs; walls; and reinforced concrete columns. Information is also given for determining the jire endurance of certain concrete members based on heat transmission criteria. Also included is information on the properties of steel and concrete at high temperatures, temperature distributions within concrete members exposed to fire, and in the Appendix, a reliability-based technique for the calculation of fire endurance requirements. Keywords: acceptability; beams (supports), columns (supports); compressive strength; concrete slabs, creep properties; heat transfer; fire ratings; fire resistance; fire tests; masonry walls; modulus of elasticity; normalized heat load; prestressed concrete; prestressing steels; reinforced concrete; reinforcing steels; reliability; stress-strain relationship; structural design; temperature distribution; thermal conductivity; thermal diffusivity; thermal expansion; thermal properties; walls.

CONTENTS Chapter I-General, p. 216R-2 1.1-Scope 1.2-Definitions and notation 1.3-Standard fire tests of building construction and materials 1.4-Application of design principles

Chapter 2-Fire endurance of concrete slabs and beams, p. 216R-4 2.1-Simply supported (unrestrained) slabs and beams 2.2-Continuous beams and slabs 2.3-Fire endurance of floors and roofs in which restraint to thermal expansion occurs 2.4-Heat transmission

Chapter 3-Fire endurance of walls, p. 216R-13 3.1-Scope 3.2-Plain and reinforced concrete walls 3.3-Concrete masonry walls This report superceded ACI 216R-81 (Revised 1987). In the 1989 revisions, an appendix has been added outlining a reliability-based technique for the calculation of fire endurance requirements of building elements. along with new Example 7, which demonstrates the use of this technique. References have been added. Discussion of this report appeared in Concrete International: Design & Construction , V. 3, No. 8, Aug. 1981, pp. 106-107 Copyright Q 1981 and 1987 American Concrete Institute. All rights reserved including rights of reproduction and use in any form or by any means including the making of copies by any photo process, or by any electronic or mechanical device, printed or written or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.

ACI Committee Reports, Guides, Standard Practices, and Commentaries are intended for guidance in designing, planning, executing, or inspecting construction, and in preparing specifications. Reference to these documents shall not be made in the Project Documents. If items found in these documents are desired to be part of the Project Documents, they should be phrased in mandatory language and incorporated into the Project Documents.

216R-1

216R-2

ACI COMMITTEE REPORT

Chapter 4-Reinforced concrete columns, p. 216R-15 4.1-General

Chapter 5-Properties of steel at high temperatures, p. 216R-16 5.l-Strength 5.2-Modulus of elasticity 5.3-Thermal expansion 5.4-Stress-strain relationships 5.5-Creep

Chapter 6-Properties of concrete at high temperatures, p. 216R-18 6.1-Compressive strength 6.2-Linear thermal expansion 6.3-Modulus of elasticity and shear modulus 6.4-Poisson’s ratio 6.5-Stress-strain relationships

CHAPTER 1-GENERAL 1.1-Scope Building codes require that the resistance to fire be considered for most buildings. The type of occupancy, the size of building and its position on the property all affect the fire resistance ratings required of various building elements. Higher fire resistance ratings often result in lower fire insurance rates, because insurance companies are concerned about fire resistance. For the most part, fire resistance ratings have been determined by the results of standard fire tests. More recently, rational design methods have been developed which allow the fire resistance to be determined by calculations (Anderberg 1978; Becker and Bresler 1977; Bresler January 1976; Bresler September 1976; Bresler 198.5; Ehm and van Postel 1967; Gustaferro 1973; Gustaferro 1976; Gustaferro and Martin 1977; lding et al. 1977; Iding and Bresler 1984; Lie and Harmathy 1972; Nizamuddin and Bresler 1979; Pettersson 1976). The rational design concept makes use of study and research into the properties of materials at high temperatures, the behavior of structures during a fire, and basic structural engineering principles. This guide illustrates the application of the structural engineering principles and information on properties of materials to determine the fire resistance of concrete construction. Generally, the information in the Guide is applicable to flat slab floors and rectangular beams. Additional materials and techniques are required for applying the design procedure given in the Guide for structural members that have other geometries. A technique for the calculation of fire endurance requirements is discussed in the Appendix.

1.2-Definitions and Notation 1.2.1-Definitions Built-Up Roofing-Roof covering consisting of at least 3ply 15 lb/100 ft2 (0.75 kg/m2) type felt and not having in excess of 1.20 lb/ft2 (5.9 kg/m2) of hot-mopped asphalt without gravel surfacing (see Section 7.3 of ASTM E 119-83). Carbonate Aggregate Concrete-Concrete made with aggregates consisting mainly of calcium or magnesium carbonate, e.g., limestone or dolomite.

6.6-Stress relaxation and creep 6.7-Thermal conductivity, specific heat, and thermal diffusivity

Chapter 7-Temperature distribution within concrete members exposed to a standard fire, p. 216R-22 7.1-Slabs 7.2-Rectangular and tapered joists 7.3-Double T units 7.4-Masonry units 7.5-Columns

Chapter 8-Examples, p. 216R-27 Chapter 9-References, p. 216R-42 9.1-Documents of standards-producing organizations 9.2-Cited references

Appendix-Design of building elements for prescribed level of fire safety, p. 216R-45

Cellular Concrete-A lightweight insulating concrete made by mixing a preformed foam with portland cement slurry and having a dry unit weight of about 30 pcf (480 kg/ m3). Cold-Druwn Steel-Steel used in prestressing wire or strand. Note: Does not include high strength alloy steel bars used for post-tensioning tendons. Critical Temperature-The temperature of the steel in unrestrained flexural members during fire exposure at which the nominal moment strength of the members is reduced to the applied moment due to service loads. End Point Criteria-The conditions of acceptance for an ASTM E 119 fire test. Fire Endurance-A measure of the elapsed time during which a material or assembly continues to exhibit fire resistance under specified conditions of test and performance; as applied to elements of buildings it shall be measured by the methods and to the criteria defined in ASTM E 119. (Defined in ASTM E 176) Fire Resistance-The property of a material or assembly to withstand fire or to give protection from it; as applied to elements of buildings, it is characterized by the ability to confine a fire or to continue to perform a given structural function, or both. (Defined in ASTM E 176) Fire Resistance Rating (sometimes called fire rating, fire resistance classification or hourly rating)-A legal term defined in building codes, usually based on fire endurance; fire resistance ratings are assigned by building codes for various types of construction and occupancies and are usually given in half-hour increments. Fire Test-See standard fire test. Glass Fiber Board-Fibrous glass roof insulation consisting of inorganic glass fibers formed into rigid boards using a binder; the board has a top surface faced with asphalt and kraft paper reinforced with glass fiber. Gypsum Wallboard Type “X"-A mill-fabricated product made of a gypsum core containing special minerals and encased in a smooth, finished paper on the face side and liner paper on the back. Heat Transmission End Point-An acceptance criterion of ASTM E 119 limiting the temperature rise of the unexposed surface to an average of 250 F (139 C) or a maximum of 325 F (181 C) at any one point.

ACI COMMITTEE REPORT

216R-4

= overall thickness of member = distance between centroidal axis and line of thrust

action [Fig. 2.3.2.1(b)] height of unit (Fig. 3.3.2.2) equivalent thickness thermal conductivity (at room temperature) Kelvins length of unit (Chapter 3) span length average face shell thickness (Chapter 3) length of span of two-way flat plates in direction parallel to that of the reinforcement being determined = bar development length = minimum measured shell thickness = fraction of weight loss of concrete = design moment = nominal moment strength at section = nominal moment strength at section at elevated temperatures = nominal positive moment strength at section at elevated temperatures = moment due to service load at section x1 = universal gas constant = heated perimeter = thrust = time = temperature compensated time = concrete cover over main reinforcing bar or average effective cover = volume of displaced water = applied load (dead + live) = unit weight of concrete = service dead load = distance from centroidal axis of flexural member to extreme bottom fiber = Zener-Hollomon parameter = = = = = = = =

= A/s = linear coefficient of thermal expansion = constant = deflection (Chapter 2) = activation energy of creep = elongation of slab due to temperamre = creep strain = creep parameter = temperature = temperature, F = temperature, C = thermal diffusivity (at room temperature) = density of concrete = density of water = fire resistance of concrete wall in natural moist con-

dition = fire resistance of masonry wall in dry condition = volumetric moisture content = Asfy/bdfc'

1.3-Standard fire tests of building construction and materials ASTM E 119 specifies the test methods and procedures for determing the fire resistive properties of building components, and is a generally accepted standard for performing fire tests. 1.3.1-Endpoint criteria of ASTM E I19 1.3.1.1-The test assembly must sustain the applied load during the fire endurance test (structural end point). 1.3.1.2-Flame or gases hot enough to ignite cotton wasie must not pass through the test assembly (flame passage end point). 1.3.1.3-Transmission of heat through the test assembly shall not increase the temperature of the unexposed surface more than an average of 250 F (139 C) or 325 F ( 181 C) at any one point (heat transmission end point). 1.3.1.4-There are additional end point criteria for special cases. Those applicable to concrete are as follows: 1.3.1.4.1-Unrestrained concrete structural members: average temperature of the tension steel at any section must not exceed 1100 F (593 C) for reinforcing bars or 800 F (427 C) for cold-drawn prestressing steel. 1.3.1.4.2-Restrained concrete beams more than 4 ft (1.2m) on centers: the temperatures in1.3.1.4.1 must not be exceeded for classifications of 1 hr or less; for classifications longer than 1 hr, the above temperatures must not be exceeded for first half of the classification period or 1 hr, whichever is longer. 1.3.1.4.3-Restrained concrete beams spaced 4 ft (1.2 m) or less on centers and slabs are not subjected to the steel temperature limitations. 1.3.1.4.4-Walls and partitions must meet the same criteria as in1.3.1.1, 1.3.1.2, and 1.3.1.3. In addition, they must sustain a hose stream test. 1.4-Application of design principles In the design of a structural member, the ratio of the load carrying capacity and the anticipated applied loads is often expressed in terms of a “factor of safety.” In designing for fire, the “factor of safety” is contained within the fire resistance rating. Thus for a given situation, a member with a 4 hr rating would have a greater “factor of safety” than one with a 2 hr rating. The introduction to ASTM E 119 states. “When a factor of safety exceeding that inherent in the test conditions is desired, a proportional increase should be made in the specified time-classification period.” The design methods and examples in this Guide are consistent with the strength (ultimate) design principles of ACI 318. BCGWC the factors of safety in design for fire are included in the resistance ratings, the load factors and strength reduction factor (Sections 9.2 and 9.3) are equal to 1.0 when designing for fire resistance.

216R-5

FIRE ENDURANCE OF CONCRETE ELEMENTS

CHAPTER 2-FIRE ENDURANCE OF CONCRETE SLABS AND BEAMS 2.1-Simply supported (unrestrained) slabs and beams 2.1.1 Structural behaviori-Fig. 2.1.1(a) and (b) illustrate a simply supported reinforced concrete slab. The rocker and roller supports indicate that the ends of the slab are free to rotate and expansion can occur without resistance. The reinforcement consists of straight bars locat d near e the bottom of the slab. If the underside of the slab is exposed to fire, the bottom of the slab will expand more than the top, resulting in a deflection of the slab. The tensile strength of the concrete and steel near the bottom of the slab will decrease as the temperature increases. When the strength of the steel at elevated temperature reduces to that of the stress in the steel, flexural collapse will occur (Gustaferro and Selvaggio 1067). Fig. 2.1.1(b) illustrates the behavior of a simply supported slab exposed to fire from beneath. If the reinforcement is straight and uniform throughout the length, the nominal moment strength will be constant throughout the length Mn = Asfy

( d - -a ) 2

Fire Fig. 2.1.1 (a)-Simply supported reinforced concrete slab subjected to fire from below

1 Fire

I&

1

(2-1)

where As is the area of the reinforcing steel fy is the yield strength of the reinforcing steel d is the distance from the centroid of the reinforcing steel to the extreme compressive fiber a is the depth of the equivalent rectangular compressive stress block at ultimate load, and is equal to Asfy/0.85fc' b where fc' is the cylinder compressive strength of the concrete and b is the width of the slab If the slab is uniformly loaded, the moment diagram will be parabolic with a maximum value at midspan wl 2 M= -

w

(2-2)

8

where w is dead plus live load per unit of length, and l is span length. It is generally assumed that during a fire the dead and live loads remain constant. However, the material strengths are reduced so that the retained nominal moment strength is (2-3) in which 0- signifies the effects of elevated temperatures. Note that As and d are not affected, but f y0- is reduced. Similarly a0is reduced, but the concrete strength at the top of the slab f c' is generally not reduced significantly. If, however. the compressive zone of the concrete is heated, an appropriate reduction should be assumed. Flexural failure can be assumed to occur when Mn0- is reduced to M. From this statement. it can be noted that the fire endurance depends on the load intensity and the strengthtemperature characteristics of steel. In turn, the duration of the fire until the “critical” steel temperature is reached depends upon the protection afforded to the reinforcement.

@ 0 hr

@ 2hr Fig. 2.1.1 (b)-Mome nt diagrams for simply supported beam or slab before and during fire exposure Usually the protection consists of the concrete cover, i.e., the thickness of concrete between the fire exposed surface and the reinforcement. In some cases, additional protective layers of insulation or tnetnbrane ceilings might be present. For prestressed concrete the nominal moment strength formulas must be modified by substituting fps for fy and Aps for As , where fps is the stress in the prestressing steel at ultimate load, and Aps is the area of the prestressing steel. In lieu of an analysis based on strain compatibility the value of fps can be assumed to be (2-4) where fpu is the ultimate tensile strength of the prestressing steel. 2.1.2 Estimating structurual fire endurance-Fig. 2. 1.2 .1 shows the fire endurance of simply supported concrete slabs as affected by type of reinforcement (hot-rolled reinforcing bars and cold-drawn wire or strand), type of concrete (carbonate, siliceous, and lightweight aggregate), moment intensity, and the thickness of concrete between the center of the reinforcement and the fire exposed surface (referred to as “u”). If the reinforcement is distributed over the tensile zone

216R-6

ACI COMMITTEE REPORT 2

I I I - CARBONATE AGG.

0 0.0

I

I 0.2

I

I 0.4

I

I

I

I 0.6

I I I I LIGHTWEIGHT AGC.

I

l

M / Mn -SILICEOUS AGG.

CA RBONATE AGG Cold Dr awn Steel

LIGHTWEIGHT

AGG

-Cold Drawn Steel

60

0.3

0.2

0.4

0.6

0.0

0.2

M / Mn

0.4 M / Mn

0.6

0.0

0.2

0.4

0.6

M / Mn

* uu = A s fy/ bd f c' ** uup= A ps fpu/bd f c'

Fig. 2.1.2.1-Fire endurance of concrete slabs as influenced by aggregate type, reinforcing steel type, moment intensity and u (defined in Section .2.1 .2) of the cross section, the value of u is the average of the u distances of the individual bars or strands in the tensile zone. The curves are applicable to the bottom face shells of hollowcore slabs as well as to solid slabs. The graphs in Fig. 2.1.2.1 can be used to estimate the fire endurance of simply supported concrete beams by using “ef,, fective u rather than “u”. Effective u accounts for beam width by assuming that the u values for corner bars or tendons are reduced by one-half for use in calculating the average u. Examples 1 and 2 (in Chapter 8) illustrate the use of Fig. 2.1.2.1 in estimating the fire endurance of a slab and a beam. Note: Gustaferro and Martin (1977) present a variety of examples using prestressed concrete. The same principles are applicable to reinforced concrete.

2.2-Continuous beams and slabs 2.2.1 Structural behavior-Structures that are continuous or otherwise statically indeterminate undergo changes in stresses when subjected to fire (Abrams et al. 1976; Ehm and van Postel 1967; Gustaferro 1970; TN0 Institute for Structural Materials and Building Structures Report No. B l-59-22). Such changes in stress result from temperature gradients within structural members, or changes in strength of structural materials at high temperatures, or both. Fig. 2.2.1 shows a continuous beam whose underside is exposed to fire. The bottom of the beam becomes hotter than the top and tends to expand more than the top. This differential heating causes the ends of the beam to tend to lift from their supports, thus increasing the reaction at the interior support. This action results in a redistribution of moments, i.e.,

the negative moment at the interior support increases while the positive moments decrease. During the course of a fire, the negative moment reinforcement (Fig. 2.2.1) remains cooler than the positive moment reinforcement because it is better protected from the fire. Thus, the increase in negative moment can be accommodated. Generally, the redistribution that occurs is sufficient to cause yielding of the negative moment reinforcement. The resulting decrease in positive moment means that the positive moment reinforcement can be heated to a higher temperature before failure will occur. Thus, it is apparent that the fire endurance of a continuous reinforced concrete beam is generally significantly longer than that of a similar simply supported beam loaded to the same moment intensity. 2.2.2 Detailing precautions-It should be noted that the amount of redistribution that occurs is sufficient to cause yielding of the negative moment reinforcement. Since by increasing the amount of negative moment reinforcement, a greater negative moment will be attracted, care must be exercised in designing the member to assure that flexural tension will govern the design. To avoid a compressive failure in the negative moment region, the amount of negative moment reinforcement should be small enough so that uu , i.e., Asfy/bdfc' is less than about 0.30 even after reductions due to temperature in fy , fc', b, and d are taken into account. Furthermore, the negative moment reinforcing bars must be long enough to accommodate the complete redistributed moment and change in the location of inflection points. It is recommended that at least 20 percent of the maximum negative moment reinforcement in the span extend throughout the span

FIRE ENDURANCE OF CONCRETE ELEMENTS

216R-7

Data: l d 2 b

u= concrete Cover +

Step l

t= Test Time

Fire

Fire

Step 2

Temperatures of Steel EC Concrete

Step 3

@ 3 hr

Fig.2.2.1-Moment diagrams for one-half of a continuous three-spun beam before and during fire exposure

(FIP /CEB Report on Methods of Assessment of Fire Resistance of Concrete Structural Members 1978). 2.2.3 Estimating structural fire e ndurance -The charts in Fig. 2. 1.2.1 can be used to estimate the fire endurance of continuous beams and slabs. To use the charts, first estimate the negative moment at the supports taking into account the temperaturcs of the negative moment reinforcement and of the concrete in compressive zone near the supports (see Fig. 2.2.3). Then estimate the maximum positive moment after redistribution. By entering the appropriate chart with the ratio of that positive moment to the initial positive nominal moment strength, the fire endurance for the positive moment region can be estimated. If the resulting fire endurance is considerably different from that originally assumed in estimating the steel and concrete temperatures. a more accurate estimate can be made by trial and error. Usually such refinement is unnecessary. It is also possible to design the reinforcement in a continuous beam or slab for a particular fire endurance period. Example 3 (in Chapter 8) illustrates this application of Fig. 2.1.2.1. From the lowermost diagram of Fig. 2.2.1, the beam can be expected to collapse when the positive nominal moment strength M+n 0- is reduced to the value indicated by the

Step 4

t As , a0- =

Step 5

d, b

Asfy00.85bf c' 0-

Mn0- = As fy0-

(d-

Fig. 2.2.3-Computational procedure for Mn0dashed horizontal line, i.e., when the applied moment at a point x 1 from the outer support Mx1 = M+n0For a uniform applied load w Mx1 =

wl x1 w x12 M n-0- x1 _ - _ -= 2

2

l

l M n-0x1 = - - 2 wl

M+n0-

216R-8

and WI? M, = --

wl?

2

v w+n*

WI?

Also X,, = zr, For a symmetrical interior bay Xl = L/2 WP M,, = 8 -M,,,

or M,=

+&

2.3-Fire endurance of floors and roofs in which restraint to thermal expansion occurs 2.3.1 Structural behavior-If a fire occurs beneath a small interior portion of a large reinforced concrete slab, the heated portion will tend to expand and push against the surrounding part of the slab. In turn, the unheated part of the slab exerts compressive forces on the heated portion. The compressive force, or thrust, acts near the bottom of the slab when the fire first occurs, but as the fire progresses the line of action of the thrust rises (Selvaggio and Carlson 1967). If the surrounding slab is thick and heavily reinforced. the thrust forces that occur can be quite large, but considerably less than those calculated by use of elastic properties of concrete and steel together with appropriate coefficients of expansion. At high ,Centroidal axis

1 -

moveable support

support

+i

Curve due to deflection of beam -

I

M

4

A Te

Fig. 2.3.1-Moment diagrams for axially restrained beam during fire exposure. Note that at 3 hr M,, is less than M and effects of axial restraint permit beam to continue to support load (Gustaferro 1970) -

temperatures, creep and stress relaxation play an important role. Nevertheless, the thrust is generally great enough to increase the fire endurance significantly. In most fire tests of restrained assemblies (Lin and Abrams 1983), the fire endurance is determined by temperature rise of the unexposed surface rather than by structural considerations, even though the steel temperatures often exceed 1500 F (815 C) (Gustaferro 1970; Issen, Gustaferro, and Carlson 1970). The effects of restraint to thermal expansion can be characterized as shown in Fig. 2.3.1. The thermal thrust acts in a manner similar to an external prestressing force, which, in effect, increases the positive nominal moment strength. 2.3.2 Estimating structural fire endurance-The increase in nominal moment strength is similar to the effect of “fictitious reinforcement” located along the line of action of the thrust (Salse and Gustaferro 1971; Salse and Lin 1976). It can be assumed that the “fictitious reinforcement” has a strength (force) equal to the thrust. By this approach, it is possible to determine the magnitude and location of the required thrust to provide a given fire endurance. The procedure for estimating thrust requirements is: (1) determine temperature distribution at the required fire test duration; (2) determine the retained nominal moment strength for that temperature distribution; (3) if the applied moment M is greater than the retained moment capacity M,,, estimate the midspan deflection at the given fire test time (if M,, is greater than M no thrust is needed); (4) estimate the line of action of the thrust; (5) calculate the magnitude of the required thrust T; (6) calculate the “thrust parameter" TIAE where A is the gross cross-sectional area of the section resisting the thrust and E is the concrete modulus of elasticity prior to fire exposure (Issen, Gustaferro, and Carlson 1970); (7) calculate 2’ defined as 2’ = A/s in which s is the “heated perimeter” defined as that portion of the perimeter of the cross section resisting the thrust exposed to fire; (8) enter Fig. 2.3.2 with the appropriate thrust parameter and 2’ value and determine the “strain parameter” &l; (9) calculate &I by multiplying the strain parameter by the heated length of the member; and (10) determine if the surrounding or supporting structure can support the thrust T with a displacement no greater than 4. Example 5 (in Chapter 8) illustrates this procedure. The above explanation is greatly simplified because in reality restraint is quite complex, and can be likened to the behavior of a flexural member subjected to an axial force. Interaction diagrams (Abrams, Gustaferro, and Salse 1971; Gustaferro and Abrams 1971) can be constructed for a given cross section at a particular stage of a fire, e.g., 2 hr of a standard fire exposure. The guidelines in ASTM E 119 for determining conditions of restraint are useful for preliminary design purposes. Basically, interior bays of multibay floors or roofs can be considered to be restrained and the magnitude and location of the thrust are generally of academic interest only. 2.4-Heat transmission 2.4.1 Single course slab thickness requirements-In addition to structural integrity, ASTM E 119 limits the average temperature rise of the unexposed (top) surface of floors or roofs to 250 F (139 C) during standard fire tests. For concrete slabs, the temperature rise of the top surface is dependent mainly upon the thickness, unit weight, moisture content,

216R-9

FIRE ENDURANCE OF CONCRETE ELEMENTS

0.0006

Panel Thickness, mm

Sanded- lightweight Concrete

Sond-Lightweight

Air -Cooled Blast

‘, Prestressed

0.0006 Carbonate Aggregote

Siliceous

Aggregate

Reinforced .

2

3

5

4

7

6

Panel Thickness, in.

Fig. 2.4.1.1-Effect of slab thickness and aggregate type on fire endurance of concrete slabs. [Based on 250 F (139 C) rise in temperature of unexposed surface]

Prestressed

OL

0.000l 600

Fig. 2.3.2-Nomogrum relating thrust, strain, and Z’ ratio (Issen, Gustaferro, and Carlson 1970) and aggregate type. Other factors that affect temperature rise but to a lesser extent, include air content, aggregate moisture content at the time of mixing, maximum size of aggregate, water-cement ratio, cement content, and slump. 2.4.1.1 Effect of slab thickness and aggregate type-Fig. 2.4.1.1 shows the relationship between slab thickness and fire endurance for structural concretes made with a wide range of aggregates. The curves are for air-entrained concretes fire tested when the concrete was at the standard moisture condition (75 percent relative humidity at mid-depth), made with air-dry aggregates having a nominal maximum size of 3/4 in. (19 mm). On the graph, lightweight aggregates include expanded clay, shale, slate, and fly ash that make concrete having a unit weight of about 9.5 to 105 pcf (1520 to 1680 kg/m3) without sand replacement. The unit weight of air cooled blast-furnace slag aggregate was found to have little effect on the resulting fire endurance of the normal weight concretes in which it is used. 2.4.1.2 Effect of unit weight-Fire endurance generally increases with a decrease in unit weight. For structural concretes, the influence of aggregate type may overshadow the effect of unit weight. For low density concretes, a relationship exists between unit weight (oven-dry) and fire endurance, as shown in Fig. 2.4.1.2. The curves in Fig. 2.4.1.2 represent average values for concretes made with dry vermiculite or perlite, or with foam (cellular concrete), with or

Oven-dry Unit 800

Wt,

kg/m3 1000

4

2

l

2 0

6 0 4 0 Oven-dry Unit Wt, pcf

80

Fig. 2.4.1.2-Effect of dry unit weight and slab thickness on fire endurunce of low density concretes. [Based on 250 F (139 C) rise in temperature of unexposed surface]

ACI COMMITTEE REPORT

216R-10

Table 2.4.2.1(a)-Data on mixes Symbol

Carb

Sil

Type of mix

Carbonate aggregate* concrete

Siliceous aggregateiconcrete

Expanded shale aggregate: concrete

Perlite aggregate concrete

374(222) 1785(1059) 1374(815) -

408(242) 1828(1085) -

446(265) 467(277) 248(147) 344(204) 1076(638) -

424(252) -

Cement. Type I. lbiyd’ (kg/m’) Coarse aggregate, Ib/yd’ (kg/m7) Medium aggregate, Ib/yd’ (kgirnj) Fine aggregate, lb&d’ (kg/m’) Sand, Ib/yd’ (hg/mi) Vermiculite aggregate, Ib/yd’ (kg/m’) Perlite aggregate, Ib/yd’ (kg/m3) Water, Ih/yd’ (kg/m3) Avg air content, percent Avg wet unit weight, pcf (kg/m3) Avg dry unit weight, pcf (kg/m3) Avg compressive strength at 28 days, psi (MPa)

4000(28)

1419(842)

i

4100(28)

LW Cellular concrete 6736(3991 216(128) 454(269)

424$$(252)

41(660) 29(465)

41(660) 30(480)

230(1.6)

420(2.9)

in. (9 mm) maximum size gravel and sand from Eau Claire, Wis. $Rotary-kiln produced expanded shale from Ottawa, Ill., ,and sand from Elgin, Ill. 5Type Ill cement. **Based on saturated surface-dry aggregates ttBascd on oven dry aggregates Mncludes weight of foam 54 Ib/yd’ (32 kg/m’) 7%

without masonry sand (Gustaferro, Abrams, and Litvin 1971). 2.4.1.3 Effect of moisture condition-The moisture content of the concrete at the time of test and the manner in which the concrete is dried affect fire endurance (Abrams and Gustaferro 1968). Generally, a lower moisture content or drying at elevated temperature 120 to 200 F (SO to 9.5 C) reduces the fire endurance. A method is available for adjusting fire endurance of concrete slabs for moisture level and drying environment (Appendix X4, ASTM E 119). 2.4.1.4 Effect of air content-The fire endurance of a concrete slab increases with an increase in air content, particularly for air contents above 10 percent. Also, the improvement is more pronounced for lightweight concrete. 2.4.1.5 Effect of sand replacement in lightweight concrete-As indicated in Fig. 2.4.1.1, replacement of lightweight aggregate fines with sand results in somewhat shorter fire endurance periods. 2.4.1.6 Effect of aggregate moisture-The influence on fire endurance of absorbed moisture in aggregates at the time of mixing is insignificant for normal weight aggregates but may be significant for lightweight aggregates. An increase in aggregate moisture increases the fire endurance. Thus, the fire endurances obtained from Fig. 2.4.1.1 represent minimum values. 2.4.1.7 Effect of water-cement ratio, cement content, and slump-Results of a few fire tests indicate that these factors, per se, within the normal range for structural concretes, have almost no influence on fire endurance. 2.4.1.8 Effect of maximum aggregate size-For normal weight concretes, fire endurance is improved by decreasing the maximum aggregate size. 2.4.2-Two-course floors and roofs 2.4.2.1-Floors or roofs may consist of base slabs of concrete with overlays or undercoatings of either insulating materials or other types of concrete. In addition, roofs generally have built-up roofing. Fig. 2.4.2.2 through 2.4.2.6 show fire endurances of various two-course floors and roofs (Abrams and Gustaferro 1969). Descriptions and symbols of the various concretes and insulating materials referred to in the figures are given in Tables 2.4.2.1(a) and 2.4.2.1(b).

2.4.2.2-Fig. 2.4.2.2 relates to various combinations of normal and lightweight concrete slabs. Note from Fig. Table 2.4.2.1(b)-Descriptions of materials and mixes Insulating concrete Cellular Concrete-A lightweight insulating concrete made by mixing a preformed foam with portland cement slurry and having a dry unit weight of about 30 pcf (480 kg/m?). Foam was preformed in a commercial foam generator. Vermiculite Concrete-A lightweight insulating concrete made with vermiculite concrete aggregate which is a laminated micaceous material produced by expanding the ore at elevated temperatures. When added to portland cement slurry, a plastic mix was formed having a dry unit weight of about 28 pcf (450 kgimj). Perlite Concrete-A lightweight insulating concrete made with perlite concrete aggregate. Perlite aggregate is produced from a volcanic rock which, when heated, expands to form a glass-like material of cellular structure. When mixed with water and portland cement a plastic mix was formed having a dry unit weight of about 29 pcf(460 kg/m3). Undercoating materials Vermiculite CM-A proprietary cementitious mill-mixed material to which water is added to form a mixture suitable for spraying. Material was mixed with 1.93 parts of water, by weight. and the mixture had a wet unit weight of 59 pcf (950 kg/m’). Sprayed Mineral Fiber-A proprietary blend of virgin asbestos fibers, relined mineral fibers and inorganic binders. Water was added during the spraying operation. Intumescent Mastic-A proprietary solvent-base spray-applied coating which reacts to heat at about 300 F (150 C) by foaming to a multicellular structure having 10 to 15 times its initial thickness. The material had a unit weight of 75 pcf ( 1200 kg/m3) and was used as received. Roof insulation Mineral Board, Manufacturer A-A rigid. felted. mineral fiber insultion board; with a flame spread rating not over 20, a fuel contributed rating not over 20. and a smoke developed rating not over 0: conforming to Federal Specification HH-I-00526 b. Mineral Board, Manufacturer B-Thermal insulation board composed of spherical cellular beads of expanded aggregate and fibers formed into rigid, flat rectangular units with an integral waterproofing treatment. Glass Fiber Board-Fibrous glass roof insulation consisting of inorganic glass fibers formed into rigid boards using a binder. The board has a top surface faced with asphalt reinforced with glass fiber and kraft. Miscellaneous Standard Built-Up Roofing-Consist:, of 3-ply, 15 lb/100 ft’ (0.73 kg/ m*) felt and not in excess of 1.20 psf (5.86 kg/m’) of hot mopping asphalt without gravel surfacing (Defined in ASTM E 119).

FIRE ENDURANCE OF CONCRETE ELEMENTS

h

216R-11

4 NORMAL W E I G H T C O N C R E T E d

v ‘4. L I G H T W E I G H T CONCRETE A .‘Q

SIL OVERLAY

CARB O V E R L A Y

T h i c k n e s s of S a n d - l i g h t w e i g h t C o n c r e t e Base Slab, mm 0

25

IO

I

5 0

7 5 100 125

0

25

50

7 5 100 0 125

I

0 1 2 3 4 2 3 4 5 T h i c k n e s s o f S a n d - l i g h t w e i g h t C o n c r e t e Base Slab, in.

5

Fig. 2.4.2.2(a)Fire endurance of normal weight concrete overlays on lightweight concrete base slabs

f.

d

L I G H T W E I G H T C O N C R E T E .J q

a ; N O R M A L W E I G H T C O N C R E T E D etc.

(3-2) (3-3)

*In practice k is oflen expressed in Btu in/h fPF; to obtain values in Btu/h ft F divide values in Btu in./h ft’F by 12.

FIRE ENDURANCE OF CONCRETE ELEMENTS

where I,),’ (I,,,,, etc. are dimensions measured on the side of minimum thickness. The values of CI and b for the shape shown in Fig. 3.3.2.2(a) arc obtained as

a = + (2u, + U?)

(3-4)

b = + (2h, + b2)

(3-5)

and for the shape shown in Fig. 3.3.2.2(b) the average web thickness is expressed as L1 = ; (2a, + NJ

(3-6)

The volumetric moisture content $ is obtained from the moisture content expressed as weight fraction m as (3-7) where 171 is usually determined by measuring the weight loss of concrete after sufficiently long heating at 22 1 F (10.5 C), Q is the density of concrete, and Q,, is the density of water, both densities in pounds per cubic foot (kilograms per cubic meter). The fire resistance of the masonry wall in dry (moistureless) condition, ‘c,,, can be calculated from the following expression:

(-$+‘yJ

t,,=

(3-8)

where ‘c,,, =

T?,, =

c,4(;)055(g ‘.?

(3-9)

(;) “.“‘( $) I.’

(3-10)

c,,

where =

c

0,205

ftl.1 h” 3.5 fiV 55/Btu0."'

0.0153m’.1

14

s035C055/J05S

and C

= I5

0.750 ft’-” h” 5 F”h/Btu”.” 0, , , 7 ml.2 +I 5 CO.“/ JO.6

in the case of solid walls T(, s T,“. The fire resistance of the concrete wall in natural (moist) condition, T, can finally be obtained from the following formula: T=

-$,I + 4t,, (1 + /3(b) 4 + T,,

(3-11)

216R-15

where fi = 5.5 for normal weight concretes and /3 = 8 .O for lightweight concretes (ASTM E 119). Example 6 (in Chapter 8) illustrates use of these equations. 3.3.3 Moisture content versus relative humidity-As is stated in Section 2.4.1.3, the amount of moisture in a specimen will affect the fire endurance. In practice, the moisture condition of the specimen is usually expressed in terms of equilibrium relative humidity (in the pores of the concrete). Appendix X4 of ASTM E 119 describes a method for calculating the moisture content from known values of the equilibrium relative humidity. 3.3.4 Effect of aggregate type and aggregate moistureSee Section 2.4.1. 3.3.5 Effect of filling cores-Fire tests show that filling the cores of hollow concrete masonry units with lightweight aggregate increases the fire endurance of the wall. In most cases a 2 or 3 hr rated wall would have its rating increased to 4 hr when the cores are filled with a lightweight aggregate. The aggregate in the cores increases the insulation value of the wall as well as provides additional moisture which absorbs heat during the fire. 3.3.6 Effect of plaster or other material on face of wallsAddition of a layer of plaster or other material to the wall increases the resistance to heat transmission, thus, increasing the fire endurance. The reader is referred to Section 2.4.2 and to UL 618 and the Expanded Shale, Clay and Slate Institute’s Information Sheet No. 14 on “Fire Resistance of Expanded Shale, Clay and Slate Concrete Masonry.” CHAPTER 4-REINFORCED CONCRETE COLUMNS 4.1-General Reinforced concrete columns have performed well during exposure to fire throughout the history of concrete construction. Columns larger than 12 in. (305 mm) in diameter or 12 in. (305 mm) square are assigned 3 hr and 4 hr fire resistance classifications in most building codes in America. It is suggested that the information in Table 4.1 be used for designing reinforced concrete columns for exposure to fire. This information is based on the results of a comprehensive series of fire tests on concrete columns (Lie, Lin, Allen, and Abrams 1984). The entire series of the test program consists of 38 full-size concrete columns. Columns designed in accordance with the requirements of Table 4.1 have been used in concrete buildings for years. These ratings combined with requirements for structural adequacy have given economical column sizes that have performed well. In the 1970s analytical procedures (Lie and Allen in NRC Technical Papers 378 and 416; Lie and Harmathy 1974) were developed for estimating temperature distributions in concrete columns during exposure to fire and for designing concrete columns for specific fire endurances and loads. CHAPTER 5-PROPERTIES OF STEEL AT HIGH TEMPERATURES Evaluating the fire endurance of concrete elements by calculations requires information on certain thermal and mechanical properties of concrete and reinforcing steel over a

ACI COMMITTEE REPORT

216R-16

Temperature C

Table 4.1-Load and performance of test columns* kN

Length of test, hr: min

Mode of failure

300

0 1300 800 710 0 170 1070 1800 1300

4: 00 2:50 3:38 3:40 5:00 3:00 3:28 2:26 3:07

None Compression " " None Buckling Compression " "

Carbonate aggre gate 10 180 11 240 12 400

800 1070 1800

8:30 6:06 3:36

" " "

Specimen no.

kips

Load

Sil iceous aggregate 0 1 2 300 3 180 4 160 5t 0 38 6t7 240 8

9

40 -

20 -

0

32

*Cross section is 12 x 12 in. (305 x 305 mm) unless otherwise indicated. tCross section is 16 x 16 in. (406 x 406 mm). t-Cross section is 8 x 8 in. (203 x 203 mm). Notes: 1. Full design load for a 12 x 12 in. (305 x 305 mm) square column is 240 kips (1070) kN). 2. Concrete cover is 11/2 in. (38 mm) to ties. 3. More test data are available from National Research Council of Canada, Ottawa, or Construction Technology Laboratones of the Portland Cement Association, Skokie, IL.

60 -

60 -

32

I

I

I

200

400

600

I 000

1

1

l000

l200

Temperature , F

Fig. 5.2-Modulus of elasticity of steel at high temperatures. Note: This curve was developed for the European Convention for Construction of Steel Structures (ECCS) (Weigler and Fischer 1964)

Cold-drawn wire of strand (ultimate )

40 -

alloy bars (ultimate

20 -

011 32

”

200

’

400

”

600

”

800

”

l000

”

l200

‘J

Fig. 5.1-Strength of certain steels at high temperatures

wide temperature range. The thermal properties of concrete form the input information for heat flow studies aimed at determining the temperature distribution in concrete elements exposed to fires. Together with information on the temperature distribution, the mechanical properties of steel and concrete provide the basis for the assessment of the structural performance of building elements during fire exposure. This chapter contains data on the elevated-temperature properties of steel. It should be noted that most of the curves presented here and in Chapter 6 represent averages of many observations. 5.1-Strength Fig. 5.1 shows the influence of temperature on the strength of certain steels. Included are data on the yield stress of structural steels (Brockenbrough and Johnston 1968) and ultimate strengths of cold-drawn steel (Abrams and Cruz 1961; Day, Jenkinson, and Smith 1960) and high strength alloy steel bars (Gustaferro, Abrams, and Salse 1971; Carlson, Selvaggio,

Fig. 5.3-Thermal expansion of ferritic steels at high temperatures

and Gustaferro 1966) used in prestressed concrete. Generally; the strengths of steels decrease with increasing temperature but ultimate strengths of hot rolled steels are often slightly higher at temperatures up to about 500 F (260 C) than they are at room temperature. 5.2-Modulus of elasticity The modulus of elasticity of steel decreases with increasing temperature as shown in Fig. 5.2 (Weigler and Fischer 1964). Modulus of elasticity for ferritic steels decreases linearly to about 750 F (400 C). Above 750 F (400 C) the modulus decreases at a higher rate. The curve in Fig. 5.2 is representative of the types of steels used in concrete construction. The average linear thermal expansio n of ferritic steels over a temperature range of 400 to 1200 F (200 to 650 C) is shown in Fig. 5.3 (U.S. Steel Corporation 1965). The coefficient of

FIRE ENDURANCE OF CONCRETE ELEMENTS

loo

80

I = 75F 2=210F 3=3OOF 4=4OOF 5=5OOF 6=6OOF

I 24C) ( 99C) (149C) (204C) (26OC) (316C)

7: 6 9 5 F ( 368 C ) 8= 8 0 0 F 1 4 2 7 C) 9 = 900F (482 C ) IO= 9 9 5 F (535 C) I I =llOOF (593C) 12=12OOF (649 C)

700

7 600

250

216R-17

(

1= 70 F ( 21 C) 2 - 2 0 0 F ( 9 3 C ) 3=300F (149C) 4=4OOF ( 2 0 4 C ) 5=495 F (257C) 6=590 F (1310C)

7 = 7 IO F 377 C) 8= 810F(432C) 9=9lOF(48BC) 10 = 1000F (538C) I I =llOOF(593C) 12=12OOF(649C)

2000

4 5 2 1500

‘S 2 0 0 8 0 t t 0-I

1

0 150

100

6_,

0

- 1000 7-

k! G

8-

5 0 100

020 0.0

0 02

0.04

0.06

0.08

0. IO

0

0.0

0.1 2

0.02

0.04

0.06

0.08

0. I O

0.12

-

Strain

Strain

Fig. 5.4.2-Stress-strain curves for prestressing steel (ASTM A 421) at various high temperatures thermal expansion is not constant over this temperature region but increases as temperature increases. The temperature dependence of the coefficient of thermal expansion GI is approximated by the formula

I

At

Constant Stress

o( = (6.1 + 0.0020-1 ) X IO-VF or o( = (11 + 0.0036H2) X IO ?C in which 8,( f$) is temperature in dcg F (C) (American Institute of Steel Construction 1980). 5.4-Stress-strain relationships Stress-strain relationships for several types of steel have been reported by Harmathy and Stanzak (1970). Such curves for an ASTM A 36 steel are shown in Fig. 5.4.1. Fig. 5.4.2 shows a family of stress-strain curves for ASTM A 421 colddrawn prestressing steel (Dorn 1954). 5.5-Creep In high-temperature processes the time-dependent nonrecoverable (plastic) unit deformation of steel is referred to as creep strain. When dealing with fire problems, it is convenient to express the creep strain according to Dorn’s concept, in terms of a “temperature-compensated time,” defined as t, = 0

where t, t AH R 0-

s

‘e-JH’R”dr

= temperature-compensated time, hours time, hours 1 activation energy of creep, J/(kg - mole) = gas constant, J/(kg * mole - K) = temperature, K

Harrnathy (1967a, 1967b) showed that the creep strain can be satisfactorily described by the following equation

Temperature-compensated

T i m e , tg

Fig. 5.5-Interpretation of creep parameters and three periods of creep

where 4 Z &IO

= creep strain = Zener-Hollomon parameter, h.l = (unnamed) creep parameter

Z and E,~ are dependent on the applied stress only (independent of temperature). Their meaning is explained in Fig. 5.5 which also shows the three periods of creep. From a practical point of view the secondary creep is the most important. (The equation given earlier for E, does not cover the tertiary creep.) Empirical equations for Z and E,, and the values of AHIR for three important steels are given by Harmathy and Stanzak (1970). Numerical techniques applying the creep information to the calculation of the deflection history of joints and beams during fire exposure have been reported (Harmathy 1967; Harmathy 1976; Pettersson, Magnusson, and Thor 1976).

216R-18

ACI COMMITTEE REPORT

Temperature, 100

F ;

C

I

Temperature, C

0 ,-

600

400

200

800

BO-

% I) 2 60 m c E * 40: ‘vly1 ? : 20 S O0

Unstressed

Residual

A v q Initial th = 3900 psi (27MPa) Aug. Initial fc of “Unsanded” Concrete= 2600 psi (18 MPa) Siliceous Aggregate Concrete I

I

1

400

k 20 E s

\

/__LI It sac 8OO 1200 Temperature, F

Fig. 6.1.1-Compressive strength of siliceous aggregate concrete at high temperature and after cooling

l

‘, \

Avg. Initial 1; of “Sanded” Concrete = 3900 psi 27 MPa) Lightweight Aggregate Concrete I

I

01

I

I

I

800

400

0

I 1200

I

J

I 600

Temperature. F

Fig. 6.1. 3-Compressive strength of lightweight concrete at high temperature and after cooling

Temperature C

Temperature, 200

300

C

400

500

600

700

5 f 60Unstressed Residual 5 * 4 0 .? 1 : E 8

Avg Initial 1; : 3900 psi (27 MPa)

zoCarbonate Aggregate Concrete

800 Temperature. F

1200

1600

Fig. 6.1.2-Compressive strength of carbonate aggregate concrete at high temperature and after cooling

0.0

L

0

200

400

600 800 Temperature. F

1000

1200

Fig. 6.2-Thermal expansion of concrete at high temperatures

CHAPTER 6-PROPERTIES OF CONCRETE AT HIGH TEMPERATURES 6.1-Compressive strength Compressive strengths ofconcretes made with different types of aggregates are shown in Fig. 6.1.1, 6.1.2, and 6.1.3 (Abrams 1971). Curves designated “unstressed” are for specimens heated to test temperature with no superimposed load and tested hot. Strengths of specimens heated while stressed to O.+f;iand then tested hot are designated “stressed to 0.4f’“. The “unstressed residual” strengths were determined from specimens heated to test temperature, cooled to room temperature, stored in air at 75 percent relative humidity for six days and then tested in compression. Note that the “stressed” strengths are higher than the “unstressed” strengths. Abrams (1971) found that stress levels of 0.25 to 0.55j’had little effect on the strength obtained. The “unstressed residual” strengths were in all cases lower than the strengths determined by the other two procedures. Abrams also noted that original concrete strengths between 4000 and 6500 psi (28 and 4.5 MPa) have little effect on the percentage of strength

retained at test temperature. In Fig. 6.1.3 the “sanded” specimens were made with sand replacing 60 percent of the lightweight fines, by volume. The “unsanded” concrete was the kind used in masonry block manufacture. Harmathy and Berndt (1966) reported data on the compressive strength of cement paste and a lightweight concrete from tests performed on specimens held at the target temperature in no-load condition for a period of 1 to 24 hr. Further data on the strength of concrete at high temperatures have been reported by Zoldners (1960); Malhotra (1956); Saemann and Washa (1957); Binner, Wilkie, and Miller (1949); and Weigler and Fischer (1964, 1968).

6.2-Linear thermal expansion Fig. 6.2 shows data on linear thermal expansion of concretes made with different aggregates. The data were obtained by Cruz using a dilatometric method but the results have not yet been published. Harmathy and Allen (1973)

FIRE ENDURANCE OF CONCRETE ELEMENTS

200

Temperature, C 400

216R-19

Temperature. 200

600

C 400

600

Carbonate e Aggregate Concrete

ui F 0 :E IJJ t9 2 WE zin% 3

60

Siliceous Aggregate Concrete w’23x106psi (16 MPa)

-

40 _

; a-” P

Lightweight Aggregate Concrete Eo= 2.6 x 106 psi ( 1 9 x10’ MPa) Siliceous Aggregate Concrete E,= 5.5 x IO6 psi ( 3 6 x.10’ MPa)

20 -

I

0 32

Lightweight Aggregate Concrete Go= 1.2 x IO6 psi (8 MPa )

I

I

400

I 800

I 1200

Temperature. F

I

I

32

I

Fig. 6.3.1-Modulus of elasticity of concrete at high temperatures

Temperature,

I

I 800

400

I200

F

Fig. 6.3.2-Shear modulus of concrete at high temperatures studied the thermal expansion of 16 different concretes used in masonry units. Among these, pumice concretes were found to exhibit considerable shrinkage at temperatures above 600 F (3 15 C). Dettling (1964) pointed out that thermal expansion of concrete is influenced by aggregate type, cement content, water content, and age. Philleo (1958) performed tests on a carbonate aggregate concrete using a different technique. He obtained somewhat higher values than those obtained by Cruz at temperatures above 700 F (370 C). 6.3-Modulus of elasticity and shear modulus Fig. 6.3.1 and 6.3.2 show the effect of high temperatures on the moduli of elasticity and shear of concretes made with three types of aggregate. The data were obtained by Cruz (1966) using an optical method. From Cruz’s data, it appears that aggregate type and concrete strength do not significantly affect moduli at high temperatures. Philleo (1958) obtained values for modulus of elasticity of a carbonate aggregate concrete using a dynamic method. His results agree closely with those obtained by Cruz up to about 700 F (370 C). From 700 to 1200 F (370 to 650 C), Philleo obtained higher values. Harmathy and Berndt (1966) and Saemann and Washa (1957) determined the modulus of elasticity in compression and found little change up to about 400 F (200 C). 6.4-Poisson’s ratio Philleo (1958) and Cruz (1966) reported data on Poisson’s ratio of concrete at high temperatures. Even though Philleo indicated a decrease in Poisson’s ratio, both he and Cruz pointed out that results were erratic and no general trend of the effect of temperature was clearly evident. 6.5-Stress-strain relationships Rather complete data between 75 and 1400 F(24 and 760 C) on stress-strain relationships in compression of a lightweight masonry concrete (expanded shale aggregate) were

3000

I

I

1

I

I

. 2000

75 F 124 Cl - 1600

5 0 0 F (260C)

1000 F (538 C) - 1200 “E

.:

1 -L

2 E -

1400 F (760 C I

i * l3ooG

- 4 0 0

* 0

0.004

0.008

0

0.017.

Strain

Fig. 6.5-Stress-strain curves for a lightweight masonry concrete at various high temperatures reported by Harmathy and Berndt (1966). Fig. 6.5 shows some of the data. Kordina and Schneider (1975) studied the stress-strain response of normal weight concretes at variable temperatures under a number of loading conditions. 6.6-Stress relaxation and creep Some data on stress relaxation and creep at high temperatures of a carbonate aggregate concrete were reported by Cruz (1968). Fig. 6.6.1 and 6.6.2 show the data graphically for a 5 hr test period. Nasser and Neville (1967) reported that age, moisture condition, type and strength of concrete, and stress-strength ratio affect creep of concrete at high temperatures. Mukaddam and Bresler (1972) and Mukaddam (1974) conducted studies on the creep of concrete at variable temperatures.

216R-20

ACI COMMITTEE REPORT

0 1.6I.6n

200

Temperature, c 400 600 I

800 1

80 ‘i ._ ‘g 6 0 ‘0 at

I \

600 F (316C)

l

$ 40 L z

20

.

Cl

l

0.0

1

o0

1

2

3

4

1

0

I

400

I

I

600 I200 Temperature, F

I 1600

Fig. 6.7.1-Thermal conductivity of four “limiting” concretes and some experimental thermal conductivity data

5

Test Time, hr

Fig. 6.6.1-Stress relaxation of a carbonate aggregate concrete 0.004

s

0002

5 8

0 0.001

Fig. 6.7.2-Volumetric specific heats of normal weight and lightweight concretes

0 0001 300F

lr4QC)

0 0.001 0

(24 Cl 0

I

I

I

I

L

I

I

I

I

I

2

3

4

i

I 5

lbst Tii hr

Fig. 6.6.2-Creep of a carbonate aggregate concrete at various temperatures [applied stress = 1800psi (12 MPa), f: = 4000 psi (28 MPa)]

6.7-Thermal conductivity, specific heat, and thermal diffusivity Harmathy (1964) developed a variable-state method by which all three of these properties of building materials can be determined from a single measuremcnt. Harmathy (1970) also presented methods for the calculation of the thermal conductivity of all kinds of concrete up to 1800 F (980 C). He defined four concretes two (No. 1 and 2) representing limit-

ing cases (from the point of view of thermal properties) among normal weight concretes, and two (No. 3 and 4) among lightweight concretes. The thermal conductivities of these four concretes. together with some experimental data. arc shown in Fig. 6.7.1. Harmathy and Allen (1973) published information on the thermal conductivity, thermal diffusivity. and specific heat of 16 masonry unit concretes for 70 to 1250 F (20 to 680 C) temperature range. Odeen (1968) studied the thermal conductivity of a concrete containing granitic aggregate. Carman and Nelson (1921) determined the thermal conductivity and diffusivity of a carbonate aggregate concrete between 120 and 390 F (50 and 200 C). Research on the specific heat of various concretes has also been reported in papers by Harmathy (1970) and Harmathy and Allen (1973). Typical ranges for the “volumetric” specific heats (product of specific heat and density) for (nonautoclaved) normal weight and lightweight concretes are shown in Fig. 6.7.2, Odeen (1968) also studied the volumetric specific heat of concrete over a temperature range up to 1800 F (980 C).

216R-21

FIRE ENDURANCE OF CONCRETE ELEMENTS

I

I

t

Carbonate Aggregate Concrete

1500

30

45

60

90

120

180

240

30

45

60

Fig. 7.1.1(a)-Temperature within slabs during, fire testscarbonate aggregate concrete CHAPTER 7-TEMPERATURE DISTRIBUTION WITHIN CONCRETE MEMBERS EXPOSED TO A STANDARD FIRE This chapter provides information on the temperature distribution in a number of concrete shapes during fire exposure, and refers to calculation techniques to be used when experimental information is not available.

90

120

180

240

Fire Test Time, min

Fire Test Time, min

Fig. 7.1.1(b)-Temperatures within slabs during fire testssilic.eous aggregate concrete

’

’

1500 c_ Sanded-llqhtweiqht

7.1- Slabs Fig. 7.1.1(a), (b), and (c) show temperatures within concrete slabs during fire tests (Abrams and Gustaferro 1968). Slab thickness did not significantly affect the temperatures except for very thin slabs or when the temperatures were less than about 400 F (200 C). Fig. 7.1.2(a), (b), and (c) show similar data for lightweight insulating concretes (Gustaferro, Abrams, and Litvin 1971). Temperatures in slabs were obtained from specimens 3 x 3 ft (0.9 x 0.9 m) in plan with protected edges. 7.2-Rectangular and tapered joists Computed and measured temperatures within rectangular beams made with quartzitic gravel have been reported (Ehm and van Postel 1967). Beam sizes tested ranged in size from 2.5 x 12 in. to 11 x 22 in. (64 x 305 mm to 280 x 560 mm). Fig. 7.2.1 through 7.2.6 show temperature distributions along the center line at various distances from the bottom of the beam and for widths up to 10 in. (254 mm) for normal weight carbonate aggregate concrete and lightweight concrete for fire endurance periods of 1, 2, and 3 hr. The width b is the beam width for rectangular members and the width at a

30

45

60

90

120

180

2 4 0

Fire Test Time, min

Fig. 7.1.1(c)-Temperatures within slabs during fire testssanded lightweight concrete

216R-22

ACI COMMITTEE REPORT

LL

P

$

1000

%

E

c”

600

45

30

Fig. 7.1.2(a)-Temperatures within 20-30 pcf (320-480 kg/ m’) lightweight insulating concrete slabs during fire tests

90

60

120

240

160

Fire Test Time, min

Fire Test Time, min

Fig. 7.1.2(c)-Temperatures within 70-80 pcf (1120-1280 kg/w-‘) lightweight insulating concrete slabs during fire tests

Width 4 mm I

too

0

I

900

IL

700

E 2 0 x 6 500 r-”

300

loin 1254mm)’ 100 3: 3

4

5

6

7

Et

9

IO

Width b, in.

Fire Test Time, min

Fig 7.1.2(b)-Temperatures within 50-60 pcf (800-900 kg/ tn-‘) lightweight insulating concrete slabs during fire tests

Fig. 7.2 .1-Temperatures in normal weight concrete rectangular and tapered units at 1 hr of fire exposure

216R-23

FIRE ENDURANCE OF CONCRETE ELEMENTS

W i d t h b , mm

loo

Width b, m m 200

150

0 1100

250 700

2-6w 100

I 200

Lightweight Concrete 900

600 1000 500 LL

5 D “p E 500 I-”

u

t

400

$ z x

300

700

: t

c

E 300

400

200

I

32 0 32

“3

4

5

6

7

1

8

I

9

3

4

I

I 6

6 5 7 Width b. in.

IO IO

I 9

10’

Width b, in

Fig. 7.2.4-Temperatures in lightweight concrete rectangular and tapered units at 1 hr of fire exposure Fig. 7.2.2-Temperatures in normal weight concrete rectangular and tapered units at 2 hr of fire exposure w i d t h b, mm

0

1400 I 200

100

Width 4 mm 150

200

250

2 Hours Lightweight Concrete - 600

1200

1000 ”

+ 600

400 32

3 Hours Normal Weight Concrete

l

300

400 $ 2 e x E I-” 300

200

200

$-- J-----JO 5 6 7 8 9 IO Width b, in

Fig. 7.2.3-Temperatures in normal weight concrete rectangular and tapered units at 3 hr of fire exposure

3 2 +-?,I------+I IO 6 7 8 9 0 3 4 5 Width b, in.

Fig. 7.2.5-Temperatures in lightweight concrete rectangular and tapered units at 2 hr of fire exposure

216R-24

ACI COMMITTEE REPORT Width b. m m

600

1000 LL

500

d ; ‘; ; 800 -

16 in. (406mm) 400

: I-” 600 -

300 3 Hours Lightweight Concrete

32

0

3

4

5

.m.

6 7 Width b , i n .

6

9

I I b-4

IO

”

Fig. 7.2.6-Temperatures in lightweight concrete rectangular and tapered units at 3 hr of fire exposure

16 in.

I (260

1200 Fl649C

7in

(178 mm)

Fig. 7.2.7-Measured temperature distribution at 2 hr of fire exposure for lightweight concrete rectangular unit

Fig. 7.2 .8-Measured temperature distribution at 2 hr of fire exposure for lightweight concrete tapered unit distance "u" from the bottom for the tapered member. These charts were generated from test data obtained from tests of rectangular and tapered members. Tests were carried out in Underwriters’ Laboratories Floor Furnace, Northbrook. Illinois, and Portland Cement Association’s Beam Furnace, Skokie, Illinois. Temperature distributions obtained in other furnaces may differ from those shown due to differences in furnace size and design, furnace wall construction, and flame type. The distributions shown in Fig. 7.2.1 through 7.2.6 were presented in this format because the chart conveniently relates the required design parameters of concrete cover, thickness, temperature, and fire endurance time. Should it be necessary to know the temperatures in the member at locations other than the center line, isotherms can be generated from the data given in Fig. 7.2.1 through 7.2.6 and from distributions obtained in test programs and computer studies completed at PCA (Lin and Abrams 1983). Sample isothermal distributions for a fire endurance period of 2 hr for lightweight aggregate concrete-rectangular and tapered sections 7 in. (178 mm) wide are shown in Fig. 7.2.7 and 7.2.8. Fig. 7.2.9 through 7.2.11 show temperature distributions in a 12 in. (305 mm) wide rectangular carbonate aggregate concrete beam. These curves were based on test temperatures developed at PCA. For members larger than 12 in. (305 mm) the temperature information shown in Fig. 7.1 for flat slabs can be used by considering the corner bars to have half the actual cover. For example, consider a 16 in. (406 mm) wide rectangular normal weight concrete beam having four equally spaced horizontal bars with 2 in. (51 mm) clear cover to the bars from the bottom of the beam and 2 in. (51 mm) clear side

216R-25

FIRE ENDURANCE OF CONCRETE ELEMENTS

16,~ IO6 mm)

IJOOF 1704C) 1500 F 1616 C ) 17OOF ,527 C)

I-

12 in.

( 305 mm)

Fig. 7.2.9 -Temperature distribution in normal weight rectangular unit at 1 hr of fire exposure

I--

12 r.

1305mml

Fig. 7.2.10-Temperature distribution in normal weight concrete rectangular unit at 2 hr of fire exposure

cover to the corner bars. The average cover is calculated as [2 + 2 + S(2) + %(2)]/4 = 1Min. [(Sl - 51 - 25 - 25)/4 = 38 mm ]. The temperature of the steel is taken from temperature distributions in the normal weight concrete shown in Fig. 7.1 for the 1.5 in. (38 mm) distance from the exposed surface. Fig. 7.2.12 and 7.2.13 show temperature distributions in carbonate aggregate concrete joists 4 in. (102 mm) wide by 16 in. (406 mm) high coated with 0.5 in. (13 mm) or 1.25 in. (32 mm) of vermiculite CM (VCM) or sprayed mineral fiber (SMF). The tests were made at the Portland Cement Association laboratories and reported by Lin and Abrams (1983). The coating materials were described by Abrams and Gustaferro (1968). 16

in.

106md

i

i

7.3-Double T Units

,/I

Harmathy (1970a) performed an extensive series of computer calculations to study the heat flow during fire tests of masonry walls. The calculations take into account the geometry of the unit, concrete type, and temperature dependent thermal properties and heat flow mechanisms.

I

.,I

I

500 F (260 C)

Odeen (1968) investigated the temperature distribution in double Ts during fire tests. Temperatures within eight sizes of double Ts have been calculated at %, 1, l%, and 2 hr of fire exposure.

7.4-Masonry units

I

,I

-

17OOF

1 9 2 7

C l ’

’ ’

i

/i ii

i i 11

I

I

Fig. 7.2.11-Temperature distribution in normal weight rectangular unit at 3 hr of fire exposure

216R-26

ACI COMMITTEE REPORT

7.5-Columns Based on a numerical technique developed by Lie and Harmathy ( 1972) the temperature distribution in concrete-protected steel columns was analyzed, and an empirical formula was derived for the calculation of the fire endurance of such

columns (Lie and Harmathy 1974). Lie and Allen, in Technical Paper 378, studied the temperature distribution in solid concrete columns during fire. Lie and Lin conducted a series of 38 fire tests of full-sized reinforced concrete columns in the period from 1976 to 1986. These latter studies covered reinforced concrete beams as well. Vermiculite Type CM (KM) 800 -

600 600 -

400 -

05

I

2

I 3

7100 4 Fire Test Time, hr

Fire Test Time, hr

Fig. 7.2 .12-Temperatures along vertical center lines at various fire exposures for 4 .0 in. (100 mm) wide rectangular units coated with SMF

Fig. 7.2.13- Temperatures along vertical center lines at various fire exposurues for 4 .O in. (100 mm) wide rectangular units coated with VCM

CHAPTER 8-EXAMPLES Six examples illustrate the calculation techniques discussed in Chapters 2 and 3 and use the data presented in Chapters 5 and 6. Example 7 shows the preliminary assessmcnt of fire endurance requirement using the technique described in the Appendix. Example 1-Determination of fire endurance of a simply supported one-way slab Given: A simply supported one-way slab reinforced with #44 Grade 60 bars on 6.0 in. (150 50 mm) centers. The slab is made of carbonate aggregate concrete with a density of 1500 pcf (2400 kgimj). Its spccitied compressive strength is 4000 Procedure Step 1-List known values

ps i (28 MPa). Cover is 0.75 in. (19 mm). The slab is 6.0 in. (150 50 mm) thick and its span is 14.8 ft (4.5 m). Live load is 100 psf (4. 8 kPa) .)

Calculation in inch-pound units Reinforcement db = 0.500 in. A,) = 0.20 in.2 As = f (0.20) = 0.40 in.Vft

Calculation in SI Metric units Reinforcement d,, = 12.7 mm Ab = 129 mm? A,

=!?$ (129) = 860

mm 2

216R-27

FIRE ENDURANCE OF CONCRETE ELEMENTS

Example 1-(Continued) Procedure Step 1-(Continued)

Calculation in inch-pound units J_i, = 60,000 psi cover = 0.75 in. u = 1.00 in.

Calculation in SI Metric units j.;, = 410 M P a cover = 19 mm 1( = 25 mm

Slab k = 6.0 in. 1 = 14.8ft 820 mmz/m width

To findi.,‘. assume that effective temperature of concrete is average of I) 1400 F (760 C) and 2) temperature of concrete at 0.38 (eff. d').

At 0.38 (4.1) + 0.9 = 2.5 in. and t = 180 minutes. 8 = 800 F

At 0.38 (102) + 23 = 62 mm and t = 180 minutes, 8 = 430 C

Find 2) using Fig 7.1. I (b)

average 8 = lW+800 2

average 8 = 760 + 430 2

= 1100 F Readf,,‘/” from Fig. 6.1.1 for concrete stressed to 0.4f,’ and calculate f,’

= 600 C

For 8 = 1100 E f,‘lf,’ = 64 percent

For 8 = 600 C, f,‘lfc’ = 64 percent

fCI ’ = 0.64(4000) = 2600psi

fL-I ’ = 0.64 (28) = 18 MW

0.44 (56,000) “’ = 0.85 (2600) (12)

921(390) ” = 0.85(18)(1000)

Calculate “- = 0.85f,‘b and compare with assumed a:

= 0.93 in. = 0.9 assumed

= 23 mm = 23 mm assumed

Step 5-Verify that qlO.30 where W, =

A*f,, b (eff.d’) f,’

%=

0.44 (56,000) 12(4.1)(2600)

921(390) WI = 1000(102)(18)

.

= 0.19 in. < 0.30 :. assumedA,a-0- of 0.9 in. and

= 0.20 < 0.30 of 0.44

. * .assumed 4 of 23 mm and A, of 390

in.2 are satisfactory

mm2 are satisfactory

x0 =

5.5 32 x0= 2 --2 5.5(5.5)

Step 6-Determine required length of top bars from

= 11.1ft

(

= 3.4m

Note: Theoretically bars could be cut a distance 1 - x0 + 1, on either side of intermediate support, where l,, is the development length of bars. However, it is recommended that only 40 percent of bars be cut off at l-%+1, on either side of the intermediate support

18 - 11.1 + 1, = 6.9 + ld

5.5 - 3.4 + 1, = 2.1 + ld

216R-32

ACI COMMITTEE REPORT

Example 3-(Continued) Procedure

Calculation in inch-pound units

Calculation in SI Metric units

Step 6-(Continued) 40 percent be cut at I! I

1 - +(, + I,

18 - ; (11.1) + I, = 12.5 ft + 1,

5.5 - 1(3.4) + I = 9.5 mm Ab = 71 mm2

A; = 1.40 in.2 (exterior support) A,- = 3.20 in.2 (interior support) A; = 3.23 in.2 (mid-span) f, = 60,000 psi cover = 0.75 in.

A-s = 903 mmz (exterior support) A,) = 2060 mm2 (interior support) A; = 2080 mm2 (mid-span) f,, = 410 MPa cover = 19 mm

FIRE ENDURANCE OF CONCRETE ELEMENTS

216R-33

Example 4-(Continued) Procedure Step 1-(Continued)

Calculation in inch-pound units

Calculation in SI Metric units u = 19+ (13 x 9.5) + (9 x 12.7) 2 x 22 = 24mm d = 152 mm

u = 0.75 + (13 x 0.375) + (9 x 0.500) 2 x 22 = 0.96 in. d = 7.0 - 0.96 = 6.0 in Slab f,,’ = 4000 psi b = 108 in. b, = 36 in. h = 7.0 in. l = 18.0 ft l,, = 16.75 ft

Slab f’ = 27.6MPa b = 2.75 m bE = 0.91 m h = 180 mm l = 5.5m ln = 5.1 m

Loading W, = 55 psf

Loading W, = 2.6 kN/m’

Wd = E (150) = 87 psf

w = 55 + 87 = 142 psf

(180/1000) (2400) (9.81) 1000 = 4.2 kN/m?

Wd =

w = 2.6 + 4.2 = 6.8 kN/m’

Step 2-Determine positive nominal moment strength A4,id at 3 hours of fire exposure from M;” = A&(d -$) To do so, values of 0, & and a; must be found Find H, using Fig. 7.1.1 (b)

For u = 0.96 in. and t = 120 min. 0 = 1200 F

For u = 24.5 mm and t = 120 min. 0 = 650 C

Determine fy0-using Fig. 5. 1

For 8 = 1200 F, j;,if, = 0.44

For 0 = 65O C, &.Jfy = 0.44

t, = 0.44 (60,000) = 26,400 psi

f;., = 0.44(410) = 180 MPa

f;.,’ = 0.81 Jo,’ = 3200 psi

f’LH ’ = 0.81 (27.6) = 22.4 MPa

A, = .f, u;.,!f? From Fig. 6.1.1 readf,, of bottom concrete Calculate a+0- from

4fw a +0- =_ 0.85x.,‘b

a + _ 3.23 (26,400) = 0.23 in. I, = 0.85 (4000) (108) ’

a’ =

P

2080(178) = 5.7 mm 0.85 (28) (2750)

Calculate nl;, from M,;, = A,j;(d - %)

IV,;@ = 3.23 (26,400) = 41,800 lb-ft/ft width = 41.8 kip-ft/ft width

/VI;,, = 2080(17X)(152 = 55.8 kN-m/m width

y)

216R-34

ACI COMMITTEE REPORT

Example 4-(Continued) Procedure

Calculation in inch-pound units

Calculation in SI Metric units

Step 3-Determine negative nominal moment strength over the exterior support from M,,, = A,&,

eff. d’ - 2 >

To do so, values of 0, &, eff. d’, and CI” must be found Find 8 using Fig. 7.1. 1 (b)

Foru = 6 in. and t = 120 min. 0 = 250 F

Forlr = 152mmandt = 120 min, N= 120 C

Determine:.f;, using Fig. 5.1

For H = 250 F, .f;,(f, = 0.95

For H = 120 C, .f;,/j; = 0.95

f,, = 0.95 (60,000)

t;.,, = 0.95 (410)

= 57,000 psi

= 390 MPa

Determine thickness of slab at 1400 F (760 C) or higher, using Fig. 7. 1. 1 (b)

0.6 in. concrete at exposed surface is at 1400 F or higher

15 mm concrete at exposed surface is at 760 C or higher

Determine effective d’

eff. d’ =

eff. d’ =

1 o.500+o.375 0-0.6-0.75-2( 2 >

7

180_ ,5_ ,+;

= 5.4 in.

(12.72+= )

= 140 mm

To hndf;“‘, assume that the realistic temperature of concrete is the average of I) 1400 F (760 C) and 2) temperature of concrete at 0.35 (eff. d') Find 2) using Fig. 7.1.1 (b)

At 0.35 (5.4) + 0.6 = 2.5 in. and t = 120 min, 8 = 600 F

At 0.35 (140) + 15 = 65 mm and t = 120 min, 8 = 320 C

Find average 0

average 0 = 1400 + 600 = 1000 F 2

average 0- =

From Fig. 6.1.1

For 0 = 1100 F, A,‘$.’ = 0.75

For 0 = 540 C, f,.,,‘$’ = 0.75

fi,,’ = 0.75 (4000) = 3000 psi

f;.,,’ = 0.75 (27.6) = 21 MPa

760- +_ 320 540 2

C

Determine negative nominal moment strength over the exterior support from a- =

”

1.4 (57,000) = 0.87 in. 0.85 (3000) (36.0)

and Mm 1.40(57,000) )I# = 1000

( > 54-0.87 . 2 12

= 33.1 kip-ft/ft width

u; =

903 (390) = 22 mm 0.85 (21) (914)

M = 903 (390) ll# 1000

140 - 22 2 1000

i = 45 kN-m/m width

1

FIRE ENDURANCE OF CONCRETE ELEMENTS

216R-35

Example 4-(Continued) Procedure

Calculation in inch-pound units

Calculation in SI Metric units

Step 4-Determine negative nominal moment strength IV,,,, over the interior support using a~ B =

AX, o.xsf;,,‘l?

(1” =

(3.23) (57,000) = 0 67 in 0.85 (3000) (108) . .

N , =

(2080) (390) = 17 mm 0.85 (21) (2740)

and M = 3.20 (57,000) NH 1000 = 77 kip-ft/ft width

M

,111

= 2064 (377.2) 1000 = 107 kN-m/m width

Step 5-Determine maximum positive bending movement M;;(,, w = 142 (18.0) = 2.56 kipift

\I’ = 6.8 (5.5) = 37 kN/m

M = u’l? = 2.56 (16.75)? 0 8 8

M = 37 (5.11) 2 0 8

= 89.8 kip-ft/ft width

= 120 kN-m/m width

A general bending moment equation can be expressed:

M = WX (1 - x) _ 33 (1 - x) 77 x 2 l l

M = wx (l - x) _ 45 (1 - x) 1 0 7 .r 2 1 1

The condition dMldx = 0 is used to determine the location of the maximum positive bending moment

dx =0 dY

dA =0 dr

Differentiating, substituting w and l, and then solving for x

_- wx-44=() Wl

2

l

x = 7.3 ft Find M;, by substituting the value of x into the moment equation

% MC, M;,“K

Step 3 - Calculate required capacity for n o r m a l i z e d heat load 6 from Fig. A.1

P

=

I.64

1’1

=

0. I

cl1

=

02 [Eq. (A-10)]

Q2

= 0.9 x 0. I = 0.09

H:; [Eq. (A-8)]

H’:I

=

\‘~(all-purpose value)

0.1 1.76.1109x1.95+0.112~11.5x10’x2x0x5.08

Qt [Eq. (A-9)]

5.08 0.24u

l109x1.95+0.223’/ll.5x104x280x5.08

2180 h”R

~~103x665+468~14.5x26x24.8

’

2 4 . 8 103~665+935~.5~26~24.X = 0.248

=

l

7 2 , 6 0 0 >“K

Step 4 - Calculate fire endurance requirement r